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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 54978.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54978.k1 | 54978d1 | \([1, 1, 0, -6922647, -7013469483]\) | \(6364379231465315641/36980976384\) | \(213187969639459584\) | \([]\) | \(1612800\) | \(2.5152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 54978.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 54978.k do not have complex multiplication.Modular form 54978.2.a.k
sage: E.q_eigenform(10)